In this paper we extend Bayesian Kullback YING YANG BKYY learning into a much broader Bayesian Ying Yang BYY learning System via using di erent sep aration functionals instead of using only Kullback Diver gence and elaborate the power of BYY learning as a gen eral learning theory for parameter learning scale selection structure evaluation regularization and sampling design with its relations to...

We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon) entropies is explained in case of non-equilibrium Smoluchowski processes. A very different temporal behav...